Here \(u=(u_1,u_2,u_3)^\top , B=(B_1, B_2, B_3)^\top \)  and \(P\)  represent the velocity field of the fluid, the magnetic field and the scalar pressure, respectively. The constants \(\mu >0\)  and \(\eta >0\)  are the viscosity coefficient and the magnetic diffusivity. The MHD system (REF )
focused here is relevant in the modeling of reconnecting plasmas (see, e.g., [1]}, [2]}, [3]}).
